Select box selects just one of multiple overlaping vertexes
Toggle X-Ray

In the 3D view header, check Toggle X-Ray (or press Alt+Z). You can now select the vertices sharing the same coordinates, but also the "backfacing" vertices (those hidden by the mesh).

Merge vertices

If you really want to merge those vertices (so your 5 independent vertices become one unique vertex), you can use the Merge by Distance feature.

Select all your vertices (A), then go to Vertex/Merge vertices/By Distance (or press Alt+M). In the Last Operator menu, you can specify the distance under which the vertices will be merged.